Using mass-selected galaxy samples from deep multiwavelength data we investigate the incidence of close galaxy pairs between z=0.4-2. Many such close pairs will eventually merge, and the pair fraction is therefore connected to the merger rate. In this analysis we distinguish between likely progenitors of “dry mergers” (two quiescent red galaxies) and those that include star-forming constituents. Over this redshift range 4-7% of log M/Msun>10.5 quiescent galaxies have a similar-mass quiescent galaxy within 30h^-1 kpc; when minor companions (1:10 mass ratio or greater) are included, the “dry” pair fraction increases to 5-15%. The mean total pair fraction, including both star-forming and quiescent companions to massive “dead” galaxies, is essentially constant (within ~10%) to z=2 for both major and minor merger candidates. If the constant pair fraction to z=2 implies a roughly constant merger rate per unit time, then most mergers in fact occur at z<1. Thus, even though other studies find major mergers to be relatively uncommon since z=1, our results suggest that few additional major mergers occur in the 1<z<2 range and other mechanisms may be required to explain the mass and size growth of galaxies over this epoch.

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